The infinity of the cardinals and of the ordinals cannot be measured by any cardinal or ordinal.

Relatedly, since every set has a cardinality less than that of its power set, there can be no set that contains everything (since such a set would already include all its subsets, and thus be at least as large as its power set). The two results imply that there cannot be a set of all ordinals or a set of all sets. In a similar way one argues that there cannot be a set of all cardinals. As a consequence of the above results we can also answer some of the questions we raised at the beginning: ther